信息表中约简补集对及其一般定义

A definition of complementary attribute reduct pairs in an information table

约简是粗糙集理论的核心研究内容,也是粗糙集区分于其他数据挖掘算法的最精彩的部分.现有约简以信息表中满足某种性质的最小属性子集为主要特征,不考虑属性集之间的相互作用和相互补充关系.从一对满足某种性质的互补属性子集出发,寻找其最小互补属性子集对,从而保障所求约简属性集对满足一定的互补性,可对实际应用中的限制条件约简进行建模.其次,从约简需保持的性质与特定划分不确定度量之间的关系出发,提出几类基本的约简补集对的一般化定义.此外,结合经典启发式约简算法,提出约简补集对的通用求解算法.最后运用一个中西医结合诊断肺炎的约简补集对求解实例说明所提算法的实用性及有效性.

Attribute reducts are an essential notion in rough set theory and one of the most distinguishing features of the rough set approaches to data mining.A reduct construction algorithm is to find a minimal set of attributes that has some property.However,it does not consider the complementary relationship between attributes.This paper proposes a general definition of complementary attribute pairs and complementary attribute reduct pairs to model a reciprocal relationship between subsets of attributes in real applications.Three primary definitions are adapted for different situations.A reduct construction algorithm is proposed for finding a complementary pair of subsets of attributes in an information table.A diagnosis and treatment example that combines traditional Chinese medicine and Western medicine is used to illustrate the practicality and usefulness of the proposed concepts at the end of this paper.